Vadim N. Gamezo

Thermonuclear Supernovae: Simulations of the Deflagration Stage and Their Implications

Large-scale, three-dimensional numerical simulations of the deflagration stage of a thermonuclear supernova explosion show the formation and evolution of a highly convoluted turbulent flame in the gravitational field of an expanding carbon-oxygen white dwarf. The flame dynamics are dominated by the gravity-induced Rayleigh-Taylor instability that controls the burning rate. The thermonuclear deflagration releases enough energy to produce a healthy explosion. The turbulent flame, however, leaves large amounts of unburned and partially burned material near the star center, whereas observations that imply these materials are present only in outer layers. This disagreement could be resolved if the deflagration triggers a detonation.

Three-dimensional delayed-detonation model of type ia supernovae

We study a Type Ia supernova explosion using large-scale three-dimensional numerical simulations based on reactive fluid dynamics with a simplified mechanism for nuclear reactions and energy release. The initial deflagration stage of the explosion involves a subsonic turbulent thermonuclear flame propagating in the gravitational field of an expanding white dwarf. The deflagration produces an inhomogeneous mixture of unburned carbon and oxygen with intermediate-mass and iron-group elements in central parts of the star. During the subsequent detonation stage, a supersonic detonation wave propagates through the material unburned by the deflagration. The total energy released in this delayed-detonation process, (1.3-1.6) × 1051 ergs, is consistent with a typical range of kinetic energies obtained from observations. In contrast to the deflagration model, which releases only about 0.6 × 1051 ergs, the delayed-detonation model does not leave carbon, oxygen, and intermediate-mass elements in central parts of a white dwarf. This removes the key disagreement between three-dimensional simulations and observations, and makes a delayed detonation the mostly likely mechanism for Type Ia supernova explosions.

Formation and evolution of two-dimensional cellular detonations

This paper reports the results of numerical simulations of cellular detonations generated by using numerical noise as a source of initial fluctuations imposed on a strong planar shock propagating through the reactive medium. The calculations show that a plane detonation wave moving at Chapman-Jouguet (CJ) velocity is unstable to transverse perturbations with wavelength greater than one or two half-reaction-zone lengths. The numerical noise affects the initial cell formation process, but it has no influence on the cell size and regularity of the structures developed. Increasing the activation energy results in more irregular structures characterized by stronger triple points, larger variations of the local shock velocity inside the detonation cell, and higher frequency of appearance and disappearance of triple points. These features of the systems with irregular cellular structures can account for the experimental observation that such systems are less affected by boundary conditions. For the two-dimensional detonation, the average reaction zone is larger and maximum reaction rate is lower than in the one-dimensional case. This means that the formation of detonation cells reduces the maximum entropy production in the reaction zone, and slows down the approach of the system to the equilibrium state. This effect is shown to increase with activation energy due to larger unreacted gas pockets, and deeper penetration of the pockets into the region of mostly burned material.

Deflagrations and detonations in thermonuclear supernovae

We study a type Ia supernova explosion using three-dimensional numerical simulations based on reactive fluid dynamics. We consider a delayed-detonation model that assumes a deflagration-to-detonation transition. In contrast with the pure deflagration model, the delayed-detonation model releases enough energy to account for a healthy explosion, and does not leave carbon, oxygen, and intermediate-mass elements in central parts of a white dwarf. This removes the key disagreement between simulations and observations, and makes a delayed detonation the mostly likely mechanism for type Ia supernovae.

The influence of shock bifurcations on shock-flame interactions and DDT

Time-dependent, multidimensional, reactive Navier-Stokes fluid-dynamics simulations are used to examine the effects of bifurcated shock structures on shock-flame interactions and deflagration-to-detonation transition (DDT) in shock-tube experiments. The computations are performed for low-pressure (100 torr) ethylene-air mixtures using a dynamically adapting computational mesh to resolve flames, shocks, boundary layers, and vortices in flow. Results of the simulations show a complex sequence of events, starting from the interactions of an incident shock with an initially laminar flame, formation of a flame brush, DDT, and finally the emergence of a self-sustained detonation with the type of transverse-wave structure that forms detonations cells. An important process, studied here in detail, is the interaction of the reflected shock with the boundary layer formed by the incident shock. This interaction leads to bifurcation of the reflected shock and the formation of a complex structure containing a leading oblique shock followed by a recirculation region. If the flame is close enough to the bifurcated structure, it becomes entrained in the recirculation region and attached to the bifurcated shock. This changes the nature of the shock-flame interaction both qualitatively and quantitatively. The reactive bifurcated structure, containing an attached flame, appears as a shock-flame complex propagating at approximately one half of the CJ velocity. The presence of a bifurcated structure leads to an increase in the energy-release rate, the formation of Mach stems in the middle of the shock tube, and creation of multiple hot spots behind the Mach stem, thus facilitating DDT.

Flame Acceleration in Narrow Channels: Applications for Micropropulsion in Low-Gravity Environments

A laminar flame propagating towards the open end of a narrow channel filled with a gaseous combustible mixture can accelerate or oscillate, depending on the wall temperature and the channel width. The accelerating flame is able to produce a high-speed flow that has the potential to provide significant thrust. We study these phenomena using multidimensional reactive Navier-Stokes numerical simulations, and show that for adiabatic walls, the maximum flame acceleration occurs when the the channel is about five times larger than the reaction zone of a laminar flame. In three-dimensional square channels, the flame speed increases roughly two times faster than in two-dimensional channels. The accelerating flame generates weak compression waves that propagate with a local sound speed and can accelerate the unreacted material ahead of the flame to the velocities close to the sound speed without creating strong shocks. This combustion regime is of particular interest for micropropulsion because it allows an efficient use of fuel and a gradual development of the trust. I. Introduction This work is based on a micropropulsion idea generated from a relatively recent discovery concerning the behavior of laminar flames propagating in very narrow tubes. When a slow laminar flame is ignited near the closed end of a tube, the material ahead of the flame is accelerated and a boundary layer is formed along the walls in the unreacted material. Due to the presence of the boundary layer, the flow velocity changes across the channel, increasing from zero at the wall to a maximum in the middle of the tube. Previous simulations [1-3] have shown that the nonuniform flow stretches the flame, so that the shape of the flame becomes similar to the velocity profile. This increases the flame surface area, thus accelerating the energy generation and the flow. There is little change in the laminar burning rate, but the speed of the flame that propagates with the flow grows very rapidly in the laboratory frame of reference, from centimeters per second to hundreds of meters per second for adiabatic walls. This phenomenon, explained by Ott et al. [1-3], is different from the well known case of flame propagation in a channel with cold walls. When the walls are cold (the case originally considered in the classical work of Mallard and Le Chatelier [4]), the flame quenches near the walls, and the flame velocity oscillates. We consider regimes in which the flame remains laminar until the end of the tube and does not produce strong shocks or detonations. The high-speed flow created by the accelerating flame has the potential to provide a significant thrust that can be further enhanced by attaching an appropriately shaped exist nozzle. The thrust will gradually increase as the flame and flow accelerate, and reach a maximum when the flame approaches the open end of the tube or the nozzle. In contrast to the majority of other combustion-based propulsion concepts, most of the thrust here can be provided by the material accelerated ahead of the flame. Therefore, a propulsion device could be only partially filled with a combustible mixture. The rest of the material can be an inert gas or combustion products from a previous pulse. This micropropulsion concept is of particular interest for low-gravity environments, where relatively small, controlled thrusts could be used for navigational corrections. In such cases, there might not be a need for the high repetition rates required for pulse combustion and pulse detonation engines. The purpose of this paper is to confirm original results [1-3] and to carry the study further to examine the possibility of using flame acceleration in narrow tubes for micropropulsion. As a model energetic system, we consider the same stoichiometric acetylene-oxygen mixture used in [3], perform numerical simulations for two-dimensional (2D) and three-dimensional (3D) channels of different widths and lengths, and analyze effects of channel sizes on integral propulsion characteristics.

De∞agration-to-Detonation Transition in H2-Air Mixtures: Efiect of Blockage Ratio

We analyze the efiect of blockage ratio on ∞ame acceleration and de∞agration-to-detonation transition (DDT) in hydrogen-air mixtures using two-dimensional numerical simulations. The numerical model is based on reactive Navier-Stokes equations coupled to a one-step Arrhenius kinetics of energy release. The simulations show that the distance to DDT does not signiflcantly change for blockage ratios BR = 0:31i0:56, but increases sharply outside of this interval. This is a result of two main competing efiects: larger obstacles promote the ∞ow and ∞ame acceleration, but they also weaken difiracting shocks. We analyze the evolution of the total energy-release rate in the system between the ∞ame ignition and the DDT and show that it grows by a factor of 1000{2000, mostly due to the ∞ame surface increase. The distance to DDT seems to be insensitive to the ignition mode, and this can be explained by the ∞ow choking that limits the in∞uence of the upstream ∞ow on the downstream.

Large-Scale Experiments and Absolute Detonability of Methane/Air Mixtures

The Gas Explosions Research Facility at Lake Lynn Experimental Mines was used to determine the detonability limit of methane for a 1-meter diameter tube as a function of the percent of methane in air. The measurements showed detonation limits of 5.3% (lean) and 15.6% (rich). A method for extrapolating these limits to larger systems, more relevant to coal mine tunnels, was proposed based on a simple scaling law and some empirical information on the number of cells required for a detonation to propagate in closed, open, and partially open geometries. The scaling law reproduces the measured detonation-cell sizes measured in the 1-m tube. Applying this to a tunnel the size of a coal mine produces a detonability limit less than the currently measured flammability limit for methane/air at atmospheric conditions, which raises interesting questions for detonation and combustion theory and suggests measurements in larger tubes.

The Influence of Chemical Kinetics on the Structure of Hydrogen-Air Detonations

Two-dimensional simulations of a detonation propagating through a 4 cm wide channel filled with a stoichiometric hydrogen-air mixture using two different models for the chemical kinetics are presented: a single-step model calibrated to compute deflagrationto-detonation transitions in hydrogen-air mixtures and a 9-species, 27-reaction mechanism specially constructed for high-pressure combustion. The detonations in both cases are qualitatively similar. Shock triple points that form along the leading edge of the front cause it to be highly corrugated and non-uniform. The trajectories of these triple points are recorded by storing the maximum pressure at each location in space. The cellular patterns formed on these numerical smoke foils are found to differ from those recorded in past experiments. The single-step model produces a hierarchy of cell structures in which the largest structures are comparable in size to experimental ones, but incomplete. Cells are incomplete at the largest scale and over an order of magnitude too small at the smallest scale. While the 27-reaction mechanism produces more regular cells, they are a factor of 3–4 smaller than those found in experiments. Agreement between the present simulation results and others found in the literature suggests that there may be a problem with using detailed thermochemical models for the extreme pressures and temperatures encountered when simulating an unstable detonation. Modifications to the single-step model parameters are presented that produce a one-dimensional detonation structure and constant volume ignition delay times that are similar to those computed using the detailed thermochemical mechanism. The two-dimensional cellular structure computed using this modified single-step reaction model is also similar to that of the 27-reaction mechanism.

Deflagration-to-Detonation Transition in Premixed H2-Air in Channels with Obstacles

We study ∞ame acceleration and de∞agration-to-detonation transition (DDT) in obstructed channels using 2D reactive Navier-Stokes numerical simulations. The energy release rate for the stoichiometric hydrogen-air mixture is modeled by one-step Arrhenius kinetics. Computations performed for channels with symmetrical and staggered obstacle conflgurations show two main efiects of obstacle spacing S. First, more obstacles per unit length create more perturbations that increase the ∞ame surface area more quickly, and therefore the ∞ame speed grows faster. Second, DDT occurs more easily when the obstacle spacing is large enough for Mach stems to form. These two efiects are responsible for three difierent regimes of ∞ame acceleration and DDT observed in simulations: (1) detonation is ignited when a Mach stem formed by the difiracting shock re∞ecting from the bottom wall collides with an obstacle, (2) Mach stems do not form, and the detonation is not ignited, and (3) Mach stems do not form, but the leading shock becomes strong enough to ignite a detonation by a direct collision with the top part of an obstacle. Regime (3) is observed for small S and involves multiple isolated detonations that appear between obstacles and play a key role in flnal stages of ∞ame and shock acceleration. For staggered obstacle conflgurations, we observe resonance phenomena that signiflcantly reduce the DDT time when S=2 is comparable to the channel width in Regime (1). Simulations also show that basic processes responsible for DDT phenomena are the same for obstructed channels and 2D arrays of obstacles, even though flnal detonation ignition modes may be difierent. Efiects of imposed symmetry and stochasticity on DDT phenomena are also considered.